Question

In an arithmetic sequence {an}, if a1 = 5 and d = 3, the first 4 terms in the sequence are
A) {9, 6, 3, 0, ...}.
B) {5, 8, 11, 14, ...}.
C) {5, 2, -1, -4, ...}.
D) {5, 15, 45, 135, ...}.

Answer 1

a1 represents the first term

d represents the common difference.....and since the common difference is 3, u have to add 3 to each term to find the next term....because with an arithmetic sequence u add to find the next term, whereas, in a geometric sequence u multiply to find the next term

5...first term
5 + 3 = 8...2nd term
8 + 3 = 11...3rd term
11 + 3 = 14...4th term

ur answer is B

Answer 2

$a_n=a_1+(n-1)d\\\\a_1=5;\ d=3\\\\substitute\\\\a_n=5+(n-1)\cdot3=5+3n-3=3n+2\\\\a_1=3\cdot1+2=5\\a_2=3\cdot2+2=8\\a_3=3\cdot3+2=11\\a_4=3\cdot4+2=14\\a_5=3\cdot5+2=17\\\vdot$

$Answer:\boxed{B)\ \{5;\ 8;\ 11;\ 14;\ 17;\ ... \} }$